ਸਮੱਗਰੀ 'ਤੇ ਜਾਓ

# ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ

${\displaystyle \scriptstyle f(t)}$
${\displaystyle \scriptstyle {\hat {f}}(\omega )}$
${\displaystyle \scriptstyle g(t)}$
${\displaystyle \scriptstyle {\hat {g}}(\omega )}$
${\displaystyle \scriptstyle t}$
${\displaystyle \scriptstyle \omega }$
${\displaystyle \scriptstyle t}$
${\displaystyle \scriptstyle \omega }$
In the first row is the graph of the unit pulse function ${\displaystyle f(t)}$ and its Fourier transform ${\displaystyle {\hat {f}}(\omega )}$, a function of frequency ${\displaystyle \omega }$. Translation (that is, delay) in the time domain goes over to complex phase shifts in the frequency domain. In the second row is shown ${\displaystyle g(t)}$, a delayed unit pulse, beside the real and imaginary parts of the Fourier transform. The Fourier transform decomposes a function into eigenfunctions for the group of translations.

ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ ਵਕਤ ਦੇ ਕਿਸੇ ਫੰਕਸ਼ਨ (ਕਿਸੇ ਸਿਗਨਲ) ਨੂੰ ਅਜਿਹੀਆਂ ਫਰੀਕੁਐਂਸੀਆਂ ਵਿੱਚ ਤੋੜ ਦਿੰਦਾ ਹੈ ਜੋ ਇਸਨੂੰ ਉਸੇ ਤਰੀਕੇ ਨਸਾਲ ਬਣਾ ਦਿੰਦੀਆਂ ਹਨ, ਜਿਵੇਂ ਕੋਈ ਸੰਗੀਤਕ ਤਾਰ ਨੂੰ ਇਸਦੇ ਰਚਣਹਾਰੇ ਨੋਟਾਂ ਦੇ ਐਂਪਲੀਟਿਊਡ (ਜਾਂ ਉੱਚੇਪਣ) ਦੇ ਤੌਰ 'ਤੇ ਦਰਸਾਇਆ ਜਾ ਸਕਦਾ ਹੈ।

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